Bayesian Belief-Network Inference Using Recursive Decomposition

Abstract: A Bayesian belief network uses a directed acyclic graph to represent
probabilistic dependencies among a set of variables. Typically, performing
inference on a belief network involves computing conditional probabilities
among variables in the network. We introduce an algorithm for belief-network
inference that is based on recursive decomposition. The algorithm recursively
bisects a belief network to create a binary tree. The tree then is used for
probabilistic inference. We describe the recursive-decomposition inference
algorithm in sufficient detail for it to be implemented readily, and we prove
the validity of the algorithm. We also link belief-network inference that is
based on recursive decomposition to the literature on vertex separators. The
recursive divide-and-conquer nature of the recursive-decomposition inference
algorithm allows an implementation that is brief and simple; it also
facilitates our analysis of the time complexity of the algorithm. A companion
paper contains an analysis and evaluation of the inference algorithm on
numerous belief network structures.